Pixels

A black$-$and$-$white computer graphics display is divided up into an array of pixels as shown below.

Each of the pixels can take on one of sixteen gray levels ranging from $0($white$)$ to $15($black$).$ In order to prevent sharp discontinuities of shade, the software system that causes pictures to be displayed enforces the rule that the gray levels of two adjacent pixels cannot differ by more than one. How many of the $256$ possible assignments of gray levels to two adjacent pixels satisfy this rule?

Pick ONE option

$34$

$9$

$10$

$11$

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